Skip to main content

Instability and Stability of Rolls in the Swift–Hohenberg Equation

Abstract:

We develop a method for the stability analysis of bifurcating spatially periodic patterns under general nonperiodic perturbations. In particular, it enables us to detect sideband instabilities. We treat in all detail the stability question of roll solutions in the two–dimensional Swift–Hohenberg equation and derive a condition on the amplitude and the wave number of the rolls which is necessary and sufficent for stability. Moreover, we characterize the set of those wave vectors which give rise to unstable perturbations.

Dedicated to Professor K. Kirchgässner on the occasion of his sixty-fifth birthday

This is a preview of subscription content, access via your institution.

Author information

Authors and Affiliations

Authors

Additional information

Received: 25 October 1996 / Accepted: 24 March 1997

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mielke, A. Instability and Stability of Rolls in the Swift–Hohenberg Equation . Comm Math Phys 189, 829–853 (1997). https://doi.org/10.1007/s002200050230

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002200050230